This past Friday, my school had an inservice day for the teachers. I was responsible for a small portion of the day. It was my task to provide a demonstration of the Four Corners differentiated instruction strategy to the rest of the faculty. I decided the best way to accomplish that was to actually go through the activity instead of just telling my colleagues about it. So of course, I based the activity on a mathematical statement. Usually, any discussion of mathematics with the faculty in general is met by moans, groans, and eye-rolling. This time, I was surprised. But I’ll get to that in a minute.Four Corners works like this:

1. Teacher writes a debateable or controversial statement on the board.
2. Students move to the corner of the room where the sign is posted that most closely represents their opinion on the statement.
3. Discussion, questions, and debate are then allowed between the four groups.
4. Next, students are allowed to switch to another corner if they changed their opinion.
5. Students are invited to explain what caused any change of opinion.

The statement I posed to the faculty was this:

There are more integers total (… -3, -2, -1, 0, 1, 2, 3, …) than there are decimal numbers just between 0 and 1.

The four statements that I posted in the four corners were:

I was quite surprised by the amount of discussion that my statement generated. It was very interesting to see how “non-math” people think about mathematics in a purely theoretical setting. The faculty really “dug” the discussion and many of them switched corners as thoughts and arguements were shared.

Ultimately, they ended up fairly evenly divided amongst the four corners. By the end of the activity, they were begging me to tell them which response was actually the correct one (I had told them that one and only one of the responses was indeed correct). I eventually did tell them. But in this post, I’ll leave it to one (or more) of my readers to leave a comment as to which response should be chosen to the above statement.

As the first quarter grading period will end this Friday, students are suddenly very interested in their grades. It’s so curious how they will wait until the last week of the grading period to ask forgiveness for the previous 8 weeks of sins. It usually sounds something like this: “Mr. B, is there anything I can do to bring up my grade?” or “Mr. B, do you have any extra credit I can do?” or “Mr. B, I really need to get a C in this class. Can I clean your board or your desks for some extra credit?”

I sure would like to get my hands on the scoundrel who invented “extra” credit.  It’s almost like extra credit is a religion that students in which students blindy place their faith — they hope that it will save them from judgement for their sins.  I just tell my students, “Sorry, you should put forth a consistent effort throughout the entire course.  Then this wouldn’t be an issue.”

Here’s an image I created — obviously playing off of the Nike logo and slogan. I have this posted on the wall in my classroom. Whenever my students start to become lazy, I just point to this sign.

Click for full-size image.

I tried something new today for a review over the basic probability chapter in my Statistics textbook. I created worksheets that contained approximately 50 exercises from the topics we have been discussing. I then assigned each problem a point value - easier problems were worth one point, harder problems were worth 3 points, and ones in the middle were worth 2 points.

Then I told the students that they had two tasks to complete today. The first was to complete 15 points worth of problems to be turned in and graded. This way, they could choose any combination of problems to solve whose combined point value was at least 15 points. The second task was for them to correctly solve a problem of their choosing and then present that solution to the class. If they chose to solve and present a 3-point problem, then they would earn 3 mythical extra credit points. If they chose to solve and present 1-point problem, they had an easier time at it, but the rewards were less (1 point extra credit).

This seemed to work very well today. The students enjoyed having the ability to choose which problems to solve. They also enjoyed listening to their peers explain solutions and rationale to the exercises.

[The phrase “mythical extra credit points” is one that I saw used by Dan Greene on his blog. As a math teacher, and I’m sure others can attest to this, I know that giving a student 3 or 5 or x extra credit points can mean as much or as little as you want it to. “Mythical” seems so fitting.]

Call 1, made at 4:22 pm while driving home from school.

Mr. B: Hello Mr. Schwartz. This is Mr. B, your daughter Jessica’s Statistics teacher. I’m calling because I’ve been having trouble with the amount of talking that Jessica has been doing in my class. Despite several one-on-one converstations with her about the importance of paying attention and not distracting others, she continues to create a disruption. If this continues, I will simply ask her to leave the class and spend the remainder of it in the principal’s office. If you are able to help the situation any from your end, I would greatly appreciate it.

Mr. Schwartz: Rest assured Mr. B, I will deal with this tonight. You will not have any other problems like this from Jessica.

Mr. B.: (Thinks to himself: Yeah, I’ve heard that before.) Thank you very much.

Call 2, made at 4:26 pm while stuck in traffic on the way home from school.

Mr. B.: Hello Ms. Clark. This is Mr. B, your daughter Markesha’s advisory teacher. I’m calling to let you know that I took Markesha’s cell phone from her today. She thought that she would try to be sneaky by hiding in the corner of my classroom and sending text-messages to her friends. She must have forgotten what I always tell my students: “You are not more sneaky than me. I know what you did, what you are doing, and what you will do.” If you would like to get the phone back for her, you may personally come by and pick it up in the main office at school.

Ms. Clark: Well, Markesha knows that she’s not supposed to use her phone in school. But I’ll speak to her about it again.

Mr. B.: Thank you. Please stress to her the fact that her phone needs to be turned off and put away in her locker while she is at school.

We’ll see if these calls actually make difference in behavior.  Sometimes they do, sometimes they don’t.

My school is one that operates on a “block” schedule. That is, one that has only four classes per day, each of which meet for one hour and twenty-five minutes. Students will take four classes in the fall semester, and then four different classes in the spring. There are some advantages to this schedule (so I’m told), but from my perspective it is a detriment to mathematics education.

In secondary mathematics, the course of study is very sequential — each class building upon skills and ideas from the previous. But what often happens to students in a block schedule is that they will take a math class during the first semester one year and then not take the next course until second semester of the next year. If you do the math, that is a full twelve months that pass with the student not taking a math course. Therein lies the major fault of block scheduling. So much can be, and usually is, forgotten during that “time off” from math.

Recently, the English department at my school has seen the need for ninth graders to take a full year of English classes. They voiced their concerns to the school leadership team and were able to get 9th grade English converted to a full year course, even though every other class remains a one-semester course. I believe the math department is close to accomplishing the same thing for Algebra 2.

Ever since our school implemented block scheduling several years ago, we have seen a decrease in the number of students enrolling in Calculus. I believe this can be attributed to the fact that students are not receiving a “continuous” mathematics education. Even the administrator in charge of the master schedule, a self-proclaimed math phobic, is beginning to see the benefits that would come with teaching Algebra 2 (if not other courses as well) for a full year.

Sometimes I wish that as a teacher I got paid by the hour. Yesterday morning started off with an 8:00am advisory team meeting (as does every Tuesday). An hour later, classes began. After a full day of classes ending at 4:00pm, the faculty had to stay another four and one-half hours. The reason for staying late was that it was our school’s first PTSA meeting of the year, immediately followed by open house. So after sitting through a arduous meeting where no one spoke loud enough to be heard, I had to entertain the parents as they cycled through their children’s classes.

Honestly though, I really do like meeting the parents of my students. It usually gives me quite a bit of insight into what makes them the way they are. Some students look just like their parents, some talk just like their parents, some smell like their parents, and some act like their parents.

Even though I enjoyed meeting the parents that made it out for open house, it was still a darn long day.

Here’s to punching the timeclock!

I’ve got a student, we’ll call him Mr. Know-it-All, who catches on very quickly to everything in his math class.  He really enjoys learning.  However, the rest of the class is trying to let him speak for them.  For example, if I ask the class a question, no one will bother answering, much less even thinking about the question, because they know that Mr. K-I-A is ready and willing to give an answer (the right one).  I’ve got to nip it in the bud before I lose everyone else.

One thought I’ve had is to let him only ask questions, but not answer any.  I think I’ll try that starting today.  Other thoughts I’ve had are to somehow let him advance at his own pace (a fast one) and not necessarily stay on track with the rest of the class; or to let him work with some of the other students in class who are struggling a bit more.  We’ll see what happens.

Today started off just as every other Monday at school. I was still sleepy and so were the students during my first period class. But like the good teacher that I am, I still found that energy that I knew the students need to see from me. Then, suddenly, my teacher energy met the devilish energy of a student in what became a bigger confrontation than I had planned for so early in the day (I think most of you teachers can attest to the fact that students in first period on Monday morning are generally pretty mellow).

As I was walking around the room, trying my best to be engaging, I spotted a young lady who was engaged in some cell phone usage. Now, she thought by keeping her cell-phone-holding hand in her purse during the text-message conversation that I would not notice the illegal behavior. But we teachers do see (and hear) everything. Feeling generous, I politely told her to put the phone away and start paying attention. This was generous, because I usually would immediately confiscate the phone — as is our school policy. But rather than accept my generosity, the young lady felt obligated to let me know that I was “trippin’” and that she did not have a phone. I asked her what, then, was she text-messaging on in her purse. She said that I must have seen a feminine hygiene product and that by my calling attention to it, I had thoroughly embarrassed her and caused her much grief. I now had no choice, in response to her direct lie and disrespect, to do my duty and confiscate the feminine hygiene product that looked like and lit up like a phone. However, she was well beyond the point of civility and cooperation, and I knew that there was no way that I was going to get that phone. My only choice was to take her to the office and let the higher-ups deal with her (our higher-ups are very supportive of us lowly teachers and I knew that they would handle the situation quickly and severely).

As luck would have it, one of the assistant principles just happened to walk into my room for some completely unrelated reason at the precise moment that the young offender was storming out in anger and “embarrassment.” I couldn’t have planned it better. After a brief conversation with the asst. principle, I was able to go right on with the lesson as if nothing had happened. The girl’s parents, however, had quite a disruption in their day. They had to come down to school for a conference with the principle. In addition to their daughter’s after-school detentions, the parents also grounded her from the cell phone indefinitely.

And to think, all of her grief could have been avoided if she had just said “yes, sir” and put her phone away when I had asked (or “axed”, as they say). *sigh* When will they learn?

This marks the eighth year in a row that the same Algebra 2 textbooks have been used in my school. The math department has missed the new textbook adoption cycle twice now due to lack of funds. So this semester, I’m not issuing textbooks at all to my Algebra 2 students. For one thing, about 40% of our books are literally being held together by duct tape or packing tape. Secondly, the text itself is lousy. It is Algebra 2: An Integrated Approach by Larson, Kanold, and Stiff. The scope of the book it too large and the sequence is not logical.

I will, instead, be encouraging the students to write their own “textbooks” by taking good notes. That’s a skill, however, that most 9th graders are severely lacking. [If only they could take notes by text-messaging on their cell phones…]  So besides the course content, I’m also teaching good note-taking strategies–emphasizing the fact that they must actually use their notes to study.

The biggest struggle for me (in not issuing a textbook) will be coming up with practice problems for the students to work.  I guess I’ll be making lots of photocopies.